Cole gave the visitors the lead with a sensational 20th minute flick from close range during a first half entirely dominated by Chelsea before Drogba, who started the match on the bench, swooped to net a contentious second with 11 minutes remaining.

A scrambled Federico Macheda goal two minutes later gave United hope of nicking a point after a much improved second half performance, but it proved too little too late as Chelsea completed the league double over the champions - and went top of the table.

Carlo Ancelotti's side now hold a two-point advantage over second-placed United with five games remaining this season. Third-placed Arsenal closed the gap on United to a single point with a last-gasp 1-0 victory over Wolves.

Chelsea's last outing came seven days ago in their 7-1 drubbing of Aston Villa, while United were in Champions League action in Germany on Tuesday - and those extra three days of rest were initially evident as Chelsea, by far the fresher side, dominated proceedings while United chased their tails for much of the first half.

The Blues, without Drogba who was not risked from the start, deservedly took the lead on 20 minutes through Cole's wonderful flick after Florent Malouda had outmuscled Darren Fletcher to get to the by-line and deliver a cross to the near post.

The goal rocked United, whose passing was uncharacteristically wayward and who, without the injured Wayne Rooney, lacked the energy to unsettle their opponents. Chelsea meanwhile were comfortable in possession, enjoying plenty of it as the sting was taken out of the Old Trafford crowd.

But United could, possibly should, have been given a lifeline back into the game on 26 minutes when Park Ji-sung was tripped in the box by Yuri Zhirkov's outstretched leg. Even though there was contact, the Korean's tumble to the floor was inelegant and failed to convince referee Mike Dean who waved play on.

The official from the Wirral, who had previously given 16 spot kicks in 24 Premier League matches this season, was again at the centre of attention four minutes later when he turned away more appeals for a penalty, this time from Chelsea. Gary Neville's barge into Nicolas Anelka at the other end was clumsy at best but Dean's refusal to award a foul was at least consistent with his earlier decision.

United slowly came back into the game as the first half wore on, culminating with a decent chance for Dimitar Berbatov to level the scores on 44 minutes, but the Bulgarian striker checked back inside as the ball fell kindly for him in the Chelsea box, allowing Frank Lampard to make a crucial challenge.

United built on that slight encouragement after the break, no doubt further inspired by an Alex Ferguson rollicking in the dressing room, giving Chelsea far less time on the ball and finally indicating that they were up for the fight.

That said, it was Chelsea who spurned a glorious opportunity to double their advantage soon after the restart, Paulo Ferreira finding himself in unfamiliar territory and one-on-one with Edwin van der Sar after a neat through pass by Cole. But the Portuguese full-back's stabbed effort rolled agonisingly wide of the post and inches beyond the outstretched boot of the late-arriving Anelka.

At the other end, Patrice Evra let fly with an ambitious volley, Park caused havoc in the Chelsea box after a surging run by Ryan Giggs and Berbatov headed wide as United applied some pressure on Petr Cech's goal for the first time in the match.

But Cech remained untested and United were made to pay as Chelsea doubled their advantage through Drogba on the break. The Ivorian striker had only been on the bench for nine minutes, but his finish was as clinical as ever as he latched onto Cole's through pass. Replays clearly showed the Ivorian to have been a yard offside as the initial pass was played, but the linesman's flag stayed down and the goal stood.

Macheda, whose impact from the substitutes' bench on the same pitch against Aston Villa last season had turned the title race in United's favour, again got his name on the scoresheet, although his goal did not have the class of his effort against Villa. This time, fellow substitute Nani teased Ferreira before delivering a dangerous ball into the box which pinged around before going in off a part of the Italian's body, possibly his hand.

But United failed to grab a point despite a frantic final few minutes during which Berbatov saw a volley saved by Cech, and must now hope Chelsea slip up in their remaining five games if they are to win an unprecedented fourth straight title.